LONDON—AstraZeneca PLC on Monday rejected what U.S. peer Pfizer Inc. said was its final increased offer, seeming to scuttle what would have been a huge trans-Atlantic pharmaceutical merger and sending the British company's shares plummeting as much as 15%.

Late Sunday, Pfizer made a final offer for AstraZeneca valued at roughly $120 billion, or £55 ($92.48) a share with a 45% cash component.